No. (1 0) is a solution. (1 1) is a solution. (1 45/77) is also a solution.

How many solutions does [tex]\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex] have? You can take any one of them, add it to (1 0) and get a solution to

No. (1 0) is a solution. (1 1) is a solution. (1 45/77) is also a solution.

How many solutions does [tex]\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}[/tex] have? You can take any one of them, add it to (1 0) and get a solution to